-1.644666506.
(a) Plot the polynomial on the interval [-2, 1]. Hand in your plot with your
assignment.
(b) Use Newton's method with a tolerance of 10-¹0 to find the root. By trying
several different initial values, x₁, determine in what interval must you choose
₁ in order achieve convergence to x*. Explain why this is the case.
(c) Determine a function g(x) so that the fixed point iteration method is guaran-
teed to converge to r*. Explain why convergence is guaranteed for your choice
of g.
(d) Using the fixed_point (...) function provided, apply the fixed point method
with this g(x) and a tolerance of 10-10.
(e) Choose ₁ -2 and compare the speed of convergence (number of iterations
to achieve tolerance) of the two methods. Does this agree with the content of
the convergence theorems for the two methods?
Fig: 1